Geared follow-up system



Aug. 3o, 1949. J. w. DAWSON 2,480,634

GEARED .FOLLOW-UP SYSTEM Filedv May 2, 1944 JOHN W. msay,

Patented Aug. 30, 1949 UNITED STATES PATENT OFFICE lGEARED FOLLOW-UPSYSTEM John W. Dawson, West Newton, Mass., assigner to RaytheonManufacturing Company, Newton, Mass., a corporation of DelawareApplication May 2, 1944, Serial No. 533,765

2 Claims. (01.'318-30) 'I'his invention relates to a variable speeddriving system in which the driven member has a relatively high inertiaand is driven through an irreversible speed reduction gear drive. Moreparticularly this invention relates to such a system in which the drivenelement is the controlled object of a servo system which has for itspurpose the driving of said controlled member to a position of agreementwith a controlling member.

Heretofore it has been deemed virtually Impossible to utilize systems ofthis kind since very frequently severe difficulties have beenencountered whenever the acceleration of the load became negative. Underthese conditions the system has tended to lock with the driven membergoing into violent oscillations and chattering.

An object of this invention is to devise a variable speed driving systemof the follow-up or servo type in which the driven member may beaccelerated and decelerated smoothly without any tendency for the`system to lock or to be sub- Jected to undesired oscillations.

Another object is to devise a servo system of the above type in whichthe agreement of positioning between the controlling and the controlledobject is secured with diminished delay and greater accuracy.

The foregoing and other objects of this invention will be bestunderstood fromvthe following description of an exemplication thereof,reference being had to the accompanying drawing, wherein:

Fig. l is a diagrammatic representation of a system embodying myinvention; and

Fig. 2 is a circuit diagram of the electrical elements of Fig. 1.

The system illustrated constitutes a servo system in which a controlledobject I is to be driven to a position of agreement with a controllingobject 2, such as a hand-operated crank. f course it is to be understoodthat this crank may be replaced by Aany movable object, the position ofwhich is to be followed by the controlled object I. The controlledobject I has considerable inertia, and is mounted on a shaft 3 which maybe supported in suitable bearings l. The shalt 3 is driven from areversible variable speed motor 5. This motor has its driving armaturemounted on a shaft 8 which drives the shaft 3 through a high-ratiogear-reduction drive consisting, for example, of a worm gear 1 mountedon the shaft 6 driving a spur gear 8 mounted on the shaft 3. The shaft 6may be mounted in suitable bearings 9. In some instances, as will bedescribed below, it may be desired to mount an additional inertia memberI0 on the shaft 8.

In order to secure the necessary servo action, controlling object 2controls a synchro II which feedsa signal corresponding to the positionof the controlling object 2 through lines I2 into a synchro I3associated with the controlled object I. As illustrated in Fig. 2, thesynchro I I is provided with Ia closed stator winding I4 carried by asuitable frame member. Said synchro I I is also provided with anarmature I5 actuated by the controlling object 2. The armature I5 isprovided with a winding I6 which is supplied with alternating currentfrom a pair of terminals I1 through a pair of leads I8. The terminals I1are connected to a suitabler source of alternating current. Threeequally-spaced points on the stator winding I4 are connected by means ofthe conductors I2 to three similarly equally-spaced points on the statorwinding I9 of the synchro I3. Said stator winding I9 is likewise carriedby a suitable frame member of the synchro I3. The synchro I3 is alsoprovided with an armature 20 mounted on the shaft 3 which, as alreadydescribed, is driven by the motor 5 through a suitable reduction gear.The armature 20 is likewise provided with an armature winding 2| whichdelivers a signal voltage through conductors 22 to a servo amplifier 23energized through a pair of conductors 24 from the alternating currentterminals I1. The servo amplifier delivers a voltage variable inmagnitude and direction to a pair of leads 25 which are connected to andenergize the motor 5. The torque exert'ed by the motor 5 will correspondboth in magnitude and direction to the voltage delivered to it by theleads 25. The servo amplifier may be of the type as described andclaimed in my copending application, Serial No. 509,631, led November 9.

1943, now Patent No. 2,423,438, dated July 8, 1947, in which themagnitude and direction of the voltage supplied to the leads 25 aredependent upon the magnitude and phase of the controlled voltagesupplied by the input conductors 22. Thus it will be seen that theoutput signal from the synchro I3 will control the speed and directionof rotation of the motor 5. As is well known, the field of the armatureI5 will be reproduced by the winding I9 of the synchro I3, and thesignal voltage delivered by the leads 22 will be a measure of thedeviation from the desired zero position of the 'armature 20 in whichsaid armature is Iat right angles to the 'magnetic iield of the windingI3. Under these conditions the servo amplifier 23 will supply current ofproper magnitude and polarity 3 to the motor 5 so as to drive thearmature 2D and thus the controlled object l to their zero position inwhich they will be in agreement with the controlling object 2.

During operation,l the controlling object 2 is moved in accordance withthe desired variations to be imparted to the position of the controlledobject l. Thereupon the motor 5 drives the object I towards its positionof agreement with the controlled object. As said position of agreementis approached, the motor 5 tends to decelerate the controlled object I.Under these conditions said controlled object, due toits inertia, tendsto overhaul the motor 5. Such a condition of overhauling causes the geardrive to pass through substantially its minimum eiciency point. The`gears l and 8 are intended to be lubricated. When such lubricated gearsare operated at a relatively high speed, oi1 films are built up on thebearing surfaces and the points of contact between the gears, so thatunder these conditions a relatively high efliciency is obtained. This isthe eiiiciency which is ordinarily considered in a gear drive. However,when operating at a minimum speed approaching zero speed, thelubrication breaks down and the friction forces may be from two to tentimes or more as great as when operating at normal speeds. Thus, underthe overhauling conditions above described, the relative speeds -of themoving gear parts will pass through zero, and therefore the gearefficiency which will be considered in the following analysis will bethe gear emciency at the minimum speed approaching zero speed.

When driving a load having a high inertia through a reduction gearhaving such a combination of low eiciency and high ratio as to beirreversible, very frequently diiiculties have heretofore beenencountered whenever the acceleration of the load becomes negative.Under these conditions, with an irreversiblev gear, the frictiondeveloped by the forces acting to retard the rotation of the highinertia load is cumulative, and the system tends to lock and stopinstantaneously. This results from the fact that the friction developedby the retarding force is proportional to the inertia and theretardation, so that if thegear is self-locking under one reversed loadcondition, it is self-locking under any other reversed load condition.The critical `condition for self-locking under reversed load is that theeiciency of the reduction gear when driving fromy the high-speed side tothe low-speed side be less than .50. In the present arrangement,therefore, due to the overhauling condition described above, theeiciency of the gear in most instances will be less than the abovecritical Value of .50.

In any practical system, some elasticity will be involved in the shaft,the gear teeth, the bearings, and the supporting elements. Heretofore,when a system involving a self-locking gear with a high inertia load wasoperated with negative acceleration, in many instances the sequence ofevents has been somewhat as follows. Upon the application of a retardingtorque lon the high-speed shaft, the system locks and comes abruptly torest. l The kinetic energy of the inertia load is stored in elasticdeformation of the assembly. Thereupon motion of the load is reversed,and the elastically-stored energy is fed back intothe kinetic energy ofthe load. During a brief interval, while travelling through thelost-motion interval, the input shaft is free and advances slightly.Thereupon the output element comes up against the opposite side of thelost-motion interval, and tries to drive the input element in thereverse direction. The locking is then repeated, and the cycle startsover again.V The result is a violent oscillation and chattering of thesystem as the driven member is decelerated. If attempts aremade toovercome the above defects by inserting elastic elements in the system,such elastic elements become very large and expensive, and subject thesystem to considerableerror, particularly where servo action isinvolved, as in the present instance.

In accordance with my invention I have discovered that if the inertiaconnected to the driving shaft is greater than a critical value, theself-locking tendency disappears and the above defects are completelyeliminated. This critical value of input inertia is such that Ia p2 11owhere I1 is the inertia of the input system, I2 is the inertia of theoutput system, p is the ratio of the driving speed to the driven speed,and no is the efficiency of the gear system at the minimum speedapproaching zero speed under sustained load.

As pointed out above, the gear efciency ordinarily involved in thepresent system will be less than .50 at any given operating speed, andunder these conditions the ratio has a finite value greater than zero.Although for values nu greater than .50 the ratio I3 may be zero,nevertheless I have found it desirable to use some inertia on the inputsystem for el'iciencies up to about .60 at any given operating speed.

In many instances sufficient inertia may be included in the drivingarmature of the motor 5 so as to satisfy Expression 1. However, wherethis inertia is insufficient for this purpose, the additional inertiaelement lil maybe used. As pointed out above, it is desirable formaximum accuracy to make the system as stiff as possible. However, someelasticity will inevitably be in- (Expression l) troduced into thesystem. The presence ofsuch K1 K2 \/TI Il where K1 and K2 arevrespectively the stiiness factors for the elastic elements in the inputand output systems. The condition of Expression 2 insures against thepossibility that the output system can lock before the inertia of theinput system takes hold to maintain themotion. If the condition ofExpression 2 is met, the motion will be smooth, while if it is not met,the motion may become irregular or oscillatory under deceleratingconditions. Since the presence of elasticity in the system is anundesirable condition, it should be understood that in attempting tosatisfy Expression 2, the stiffness of the out- (Expression 2) putsystem should not be decreased but rather 'y the stiffness of the inputsystem should be increased.

If the system, as illustrated in Figs. 1 and 2, is constructed so thatthe inertia of the input system is greater than the above-describedcritical value, and if the stiffness factors satisfy the necessaryrelationship, as called for by Expression 2, the system will operatesmoothly and without the diilculties which the art has heretoforeencountered.

It is to be understood that this invention is particularly effective inthose systems in which the inertia of the output system is so high thatalthough it satises the requirements of Expression l, it neverthelesstends to approach the critical value above which Expression 2 is nolonger satislied. Therefore in Expression 1 the ratio of the inertlas isof the order of magnitude of the righthand side of said expression,although numerically smaller than said right-hand side. l Of course itis to be understood that this invention is not limited to the particulardetails as described above as many equivalents will suggest themselvesto those skilled in the art. It is accordingly desired that the appendedclaims be given a broad interpretation commensurate with the scope ofthe invention within the art.

What is claimed is:

1. A follow-up system comprising a controlling member adapted to bemoved in accordance with a desired variation, a controlled member, avariable speed driving means for said controlled mexnber, a high ratiospeed reduction irreversible mechanism interposed between said drivingmeans and said controlled member, means for causing said driving meansto drive said controlled member to a position of agreement with saidcontrolling member, the inertia of tthe output system driven by saidmechanism being of the order ot and less than the inertia of the inputsystem feeding into said mechanism being greater than of the drivingspeed to the driven speed oi' said mechanism, and 11 is the eiiiciencyof said mechaand less than to Ilp2 l 2m the inertia of the input systemfeeding into said mechanism being greater than where I1 is the inertiaof said input system, Iz is the inertia of said output system, p is theratio of the driving speed to the driven speed of said mechanism, and11o is the eiliciency of said mechanism at a minimum speed approachingzero speed under sustained load, the stiffness of said input and outputsystems being such that is much greater than 11, I1 where K1 and K1 arethe stiffness factors respectively of said input and output systems.

JOHN W. DAWSON. mlmmnuonsY CITED The following references are of recordin the ille of this patent: v

UNITED STATES PATENTS Number Name Date Re. 16,667 Hewlett et al July 5,1927 1,554,698 Alexanderson Sept. 22, 1925 1,684,138 Nixdorn sept. 11,1928 1,847,181 Harrison Mar. 1. 1932 1,922,759 Davis Aug. 15. 1933

